Topological Materials for Spintronis - JAEA...Topological insulator H surface k y x k x y Voltage difference between leftand right spin‐electricity conversion spin‐momentum locking

Seminar at JAEA, 23rd Jan. 2017

Topological Materials for SpintronisTopological Materials for Spintronis

Kentaro Nomura (IMR, Tohoku University)

トポロジカル物質におけるスピントロニクス現象

Topological Materials for SpintronisTopological Materials for Spintronisトポロジカル物質におけるスピントロニクス現象

Collaborators

Yasufumi Araki, Gerrit Bauer, Koji Kobayashi, Daichi Kurebayashi,

Ryota Nakai, Yuya Ominato, Akihiko Sekine,Nobuyuki Okuma(Tokyo)

Yuki Shiomi (Tohoku), Eiji Saitoh (Tohoku), Yoichi Ando (Cologne)


Topological Materials for SpintronisTopological Materials for Spintronisトポロジカル物質におけるスピントロニクス現象


• Topological insulators

3D Topological insulator

E

kx

ky

kz

E

kxkz

ky

• Weyl semimetals

Take home message

TCS AHEV(t)M B

Kurebayashi, KN 2016

z

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)

V(t)

(magnetic) Weyl semimetal

Tim e [nsec]

0

0.2

0.4

0.6

-1.5-1

-0.5

0 0.5

1

1.5

0 50 100 150 200

Inp

ut voltage [

V ]

(a)

Magnetization switchingvia electric voltage

Outline

• Introduction: What is a Weyl semimetal?

• Magnetization dynamics in Weyl semimetals

Part I

Part II

• Spin-Electricity conversion in topological insulators


E

kx

ky

Kane-Mele, Bernevig-Hughes-Zhang, Moore-Balents, Roy, Fu-Kane-Mele, …

Topological insulators

strong SOCweak SOC

E

+

_ +

_

Normalinsulator

Topologicalinsulator


E

kx

ky

Topological insulators

strong SOCweak SOC

E

+

_ +

_

Normalinsulator


3d Topological insulator materials• Bi1‐xSbx• Bi2Se3, Bi2Te3• Bi‐Sb‐Te‐Se (BSTS)

Spintronics phenomena on TI surface

A.R.Mellnik, et al. Nature 511, 449‐451 (2014)

Shiomi, et al. Phys. Rev. Lett. 113, 196601 (2004)C.H.Li, et al. Nature Nano. 9, 218‐224 (2014)Y. Fan, et al. Nature Materials 13, 699 (2014)Kondo et al. Nature Phys. 3833 (2016)

Experimental studies

Spintronics phenomena on TI surface

Experimental studies

Topological insulator

E

kx

ky

Spin injection experiments

Hsurface ky x kx y

spin‐momentum locking

z : , real spin

Voltage difference between left and right

spin‐electricity conversion


E

kx

ky+

++

+

__

__


Hsurface ky x kx y




z : , real spin



Hsurface ky x kx y




Y. Shiomi, et al. PRL 113, 196601 (2014)

z : , real spin


++

++

__

__

Hsurface ky x kx y




Y. Shiomi, et al. PRL 113, 196601 (2014)

z : , real spin


____



Y. Shiomi, et al. PRL 113, 196601 (2014)



++

++

__

__


____

Dumping enhancement• Local spins

++

++

__

__


____

• Surface electrons

• Local spins

a JevF

ẑ S

Dumping enhancement

++

++

__

__


____

a JevF

ẑ SdSdt

H eff S (0 )SdSdt

The enhanced dumping factor

• Local spins

Dumping enhancement

++

++

__

__


____

a JevF

ẑ S


3108.7~

dSdt

H eff S (0 )SdSdt

Dumping enhancementY. Shiomi, et al. PRL 113, 196601 (2014)

++

++

__

__


____

J ≅ 10 meV

Microscopic theory of spin torque

Relation between

surface and x

y

z

__

__


E (electric field)

exert a spin torque on the local spin magnetization

EEdelstein effect

N. Okuma, KNarXiv:1610.05236


Torque at the surface

Relation between

surface and x

y

z

__

__


E (electric field)



Torque at the surface

x

y

z

__

__


E (electric field)


Microscopic theory of spin torqueLinear response theory

= +S A

Sy

Sz

0

x

y

z

__

__


E (electric field)



= +S A S

S

A +



= +S A S

S

A +

ckck G(k)

Sqi Sq

j ij (q)

(q,n)

G(k,)

G(k‐q,n)



= +S A S

S

A +

(q,n)

G(k‐q,n)


__

__


E (electric field)

Short summary


__

__


E (electric field)



Electrically induced spin current

Part I

Outline

• Introduction: What is a Weyl semimetal?

• Magnetization dynamics in Weyl semimetals

Part I

Part II


kykx

E

KK’

K’K’

K

K

What is Weyl a semimetal?

3-dimensional analogue of “graphene”

H2D = pxx + pyy

H3D = pxx + pyy + pzz

2D (Graphene)

3D (Weyl semimetal)

Murakami (2007)Wan et al. (2011)Burkov&Balents (2012)Halasz&Balents (2012)….

E(p) vF px2 py

2 pz2

E(p) vF px2 py

2Wallace (1947)

What is Weyl a semimetal?

H2D = pxx + pyy

2D (Graphene)


3D (Weyl semimetal)

i : pseudo-spin

sublattice degrees of freedom

i : real-spin

magnetic degrees of freedom

Differences

(Weak SOC)

(Strong SOC)

Theory and Experiment

Wan et al. (2011)Murakami (2007)Burkov, Balents (2012)


3D (Weyl semimetal) i : real-spin

magnetic degrees of freedom

(Strong SOC)

Huang et al. (2015)Xu et al. (2015)Souma et al. (2016)

E

pxpy

E2 px2 py

2 pz2 m0

2

particle

hole

H px1py2 pz3 m04

• Dirac theory

Relativistic quantum mechanics

E

pxpy

E2 px2 py

2 pz2 m0

2

{i , j } 2ij

H2 pi i m04i

2

pipj i ji, j pim0( i4 4 i )

i m0244

H px1py2 pz3 m04

• Dirac theory


matrices

E

pxpy

E2 px2 py

2 pz2 m0

2

{i , j } 2ij

H2 pi i m04i

2


i m0244

H px1py2 pz3 m04

• Dirac theory

x zy

x 0 11 0

y

0 ii 0

z

1 00 1

matrices


E2 px2 py

2 pz2 m0

2

{i , j } 2ij

H px1py2 pz3 m04

• Dirac theory

H2 pi i m04i

2


i m0244

00 ,

00 ,

00 ,

00

1 2 3 4

E

pxpy

i: 4x4 Dirac matrices


• Weyl theory• Dirac theory

H px1py 2 pz 3

i: 2x2 Pauli matrices

H px1py2 pz3 m04

E

pxpy

massless

E

px py

i: 4x4 Dirac matrices


E

pxpy

massless

E

px py

H px1py 2 pz 3H px1py2 pz3 m04

• Weyl theory• Dirac theory


i: 2x2 Pauli matricesi: 4x4 Dirac matrices

degenerate non-degenerate

m0=0 (massless) massless

Dirac-Weyl semimetals

H px1py 2 pz 3H px1py2 pz3 m04

• Weyl semimetal• Dirac semimetal

i: 2x2 Pauli matricesi: 4x4 Dirac matrices



symmetry breaking

pzpy

Dirac-Weyl semimetals

• Weyl semimetal• Dirac semimetal

Two types of Weyl semimetals

• Weyl semimetal with broken space‐inversion symmetry

Non‐magnetic M=0

Ferromagnetic M ≠ 0

• Weyl semimetal with broken time‐reversal symmetry

‐Materials: TaAs , NbAs, NbP, TaP, ..

‐Only theoretical proposals so far

From TI to Weyl SM

Ferromagnetic M ≠ 0

• Weyl semimetal with broken time‐reversal symmetry

‐Only theoretical proposals so far

M ≠ 0

Magnetic Weyl semimetalTopological insulator

magnetic doping

strong SOCweak SOC

E

+

_ +

_

Normalinsulator


From TI to Weyl SM

strong SOCweak SOC

E

+

_ +

_

Normalinsulator


Dirac semimetal

degenerate

From TI to Weyl SM

strong SOCweak SOC

E

+

_ +

_

Normalinsulator


Dirac semimetal

degenerate

magneticdopants

From TI to Weyl SM


Burkov, Balents 2011

magnetic doping

• Weyl semimetals• Dirac semimetals

pzpy

From TI to Weyl SM

0

10

20

30

40

50

60

70

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

Tem

pera

rture

[K]

M0 [eV]

high T

low T

TheoryKurebayashi, KN. (2014)

Dirac semimetal

Weyl semimetal

M ≠ 0M = 0degenerate non-degenerate

paramagnetic ferromagnetic

0

+

_ +

_

Magnetic ordering

Science 339, 1582 (2013)

Bi2‐yCry(Se1‐x Tex)3

Cr

Experiment+

_+

_


Science 339, 1582 (2013)

Experiment+

_+

_


F 12s

M2 12e

m2 JMm

12

1s

J2e

M

2 12e

m e JM 2

local spin electron spin



Magnetic ordering

F 12s

M2 12e

m2 JMm

12

1s

J2e

M

2 12e

m e JM 2

local spin electron spin



> 0

12

1

GL & gradient expansion

Araki, KN, PRB 93, 094438 (2016)

strongweak

HWeyl ·

Hexc ·

M ≠ 0non-degenerate

ferromagnetic

12

1

GL & gradient expansion

strongweak

Hexc ·

Hedgehog Radial vortex∇M ≠ 0, ∇×M = 0 ∇M ≠ 0, ∇×M = 0

Excited states

Araki, KN, PRB 93, 094438 (2016)

HWeyl ·

Anomalous transport phenomena

• Anomalous Hall effect

in magnetic Weyl semimetals

• Chiral magnetic effect

B jCME

Fukushima, Kharzeev, and Warringa (2008)

Mz ≠ 0jAHE

E

Anomalous Hall responses

janomaly AHE

M×E

ky

kxkz

b(k)

+_

kz

E

22

2

· 00 ·

Mz ≠ 0jAHE

E


janomaly AHE

M×E anomaly AHE M B

Mz ≠ 0

anomalyB

+ + + + ++ + + + +

+ + + + +

+ + +

+

anomaly janomaly

Mz ≠ 0jAHE

E


janomaly AHE


Mz ≠ 0

anomalyB

_ _ _ _ __ _ _ _ _

_ _ _ _ ___ _

_

anomaly janomaly

Mz ≠ 0jAHE

E

0

anomaly


janomaly AHE


anomaly

BM

0

anomaly anomaly

Landau levels

Chiral anomaly1D Weyl fermions

k

Energy

dkdt

eEk

Energy

H1D dx R ix eAx RL ix eAx L

L R

Chiral anomaly

dNRdt

dx e2 E

1D Weyl fermions

k

Energy

k

Energy


L R

dNLdt

dx e2 E

dkdt

eE

Chiral anomaly

d(NRNL)dt

dxe E

d(NRNL)dt

axial charge

total charge0

1D Weyl fermions


dNRdt

dx e2 E

dNLdt

dx e2 E

kz


d(NRNL)dt

0

axial charge

total charge

d(NRNL)dt

dxe E

for 1D

B = 0


d(NRNL)dt

0

axial charge

total charge

L R NLL BLxLyhc / e

d(NRNL)dt

dxe E

for 1D

B ≠ 0


d(NRNL)dt

0

axial charge

total charge

d(NRNL)dt

d3x 2e2

(2 )2E B

L R NLL BLxLyhc / e

B ≠ 0


d(NRNL)dt

d(NRNL)dt

d3x 2e2

(2 )2E B

0

axial charge

total charge

a = JM “chiral vector potential”

L R


d(NRNL)dt

d(NRNL)dt

a = JM “chiral vector potential”

d3x 2e2

(2 )2(E B e b)

JM

d3x 2e2

(2 )2(E be B)

Zyusin & Burkov (2012), Liu, Ye, Qi (2013)

Chiral anomaly

d(NRNL)dt

d(NRNL)dt

d3x 2e2

(2 )2(E be B)

d3x 2e2

(2 )2(E B e b)

JM

j e

2

2 2(E b e B)


Chiral anomaly

d(NRNL)dt

d(NRNL)dt

d3x 2e2

(2 )2(E be B)

d3x 2e2

(2 )2(E B e b)

JM janomaly


j e

2

2 2(E b e B)

Chiral anomaly

JM janomaly

janomaly e2

2 2JM E

anomaly e2

2 2JM B


janomalyE

Mz ≠ 0

j e

2

2 2(E b e B)

Weyl fermions in B field

NLL BLxLyhc / e

0th Landau level :

nth Landau level :

(n=±1, ±2, ±3,…)

MM

AHE AHEM̂ Bcharge density

0LL

(not resistivity)

0LL

· · ·

Gate-tuned magnetization dynamics

Charging Gate voltage

Zeeman Anisotropy

z

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)

anomaly AHE M B

V(t)


· · ·

Zeeman Anisotropy

z

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)

Charging Gate voltage12

charge density


anomaly AHE M B

V(t)


· · ·


Zeeman Anisotropy

Zeeman

Charging

z

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)

Mx

My

MzB


V(t)


· · ·


Zeeman Anisotropy

z

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)

Charging

Charging

Mx

My

MzB

Zeeman


+ + + + + + + +

_ _ _ _ _ _ _ _V(t)


· · ·


Zeeman Anisotropy

z

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)

V


· · ·


Zeeman Anisotropy

z

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)

V > 0

Charging

Mx

My

MzB

TCS AHEV(t)M B


+ + + + + + + +

_ _ _ _ _ _ _ _

V(t)

Charge‐induced spin torqueKN, Kurebaashi, 2015


· · ·


Zeeman Anisotropy

z

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)

V > 0

Charging

Mx

My

MzB

TCS AHEV(t)M B


V(t)


z

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)

V > 0

Charging

Mx

My

MzB

TCS AHEV(t)M B


V(t)


z

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)

Tim e [nsec]

0

0.2

0.4

0.6

-1.5-1

-0.5

0 0.5

1

1.5

0 50 100 150 200

Inp

ut voltage [

V ]

(a)

TCS AHEV(t)M B


V(t)


spin current

jspin gr

4

M̂

dM̂dt

(b )

B

Metal

Insulator

W SM

Metal

V(t)

-15

-1-0.5

0 0.5

1

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1(b ) B

Tim e [nsec]

Inp

ut voltage [

V ]

-0.015-0.01

-0.005 0

0.005 0.01

0.015

-0.004-0.002

0 0.002 0.004 0.006 0.008 0.01

0 0.5 1 1.5 2Kurebayashi, KN 2016

AC voltage

V(t) > 0

V(t)

Chiral magnetic effect

00

pz

·

· ·

py · ·

Anomalous Hall effect

Chiral magnetic effect

Chiral magnetic effect vanishes in equilibrium

M

Inhomogeneous Weyl semimetal

real space

antiparallel parallel

Doped local spins

Inhomogeneous Weyl semimetal

kx

kz

kxky

real space

k space


Magnetotransport in Weyl semimetal

kx

kz

kxky

real space

k space

I


I

↑↓ 0 ↑↑ 0

Ideal magnetotransport!

Transmission probability from left to right is zero

Magnetotransport in Weyl semimetal

kx

kz

kxky

real space

k space

I


disorder

I

↑↓

↑↑

cond

uctance

K. Kobayashi

Domain wall in Weyl semimetal

Axial vector potential

·

· ·

0Axial magnetic field

A. YoshidaY. Araki



·

· ·

0

2

Equilibrium current

Axial magnetic field



·

· ·

0

2

Equilibrium current

2

Chiral magnetic effectc.f.



Yasufumi Araki et al. (2016)

·

· ·

Electric charge on the domain wall

Electrical domain wall motion

Magnetic Weyl semimetal

E field


↑↓ 0

Electrical domain wall motion

Magnetic Weyl semimetal

A less-dissipation spintronics device


E(t)

Chiral magnetic effects

2

/

/

2

B ≠ 0


2

2

/

/

Electrical current

22

B ≠ 0


2

2

/

/

2

Electrical current Axial current

2 2


2

00 ·

2

Spin density Axial current

D. Kurebayashi


Charge‐induced spin torque

z

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)

V(t)

Local spin magnetization

2

Spin density

D. Kurebayashi


Charge‐induced spin torque

z

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)

V(t)

Local spin magnetization

Tim e [nsec]

0

0.2

0.4

0.6

-1.5-1

-0.5

0 0.5

1

1.5

0 50 100 150 200

Inp

ut voltag

e [

V ]

(a)

D. Kurebayashi

Summary• We demonstrated magnetization switching

and spin pumping by the charge-induced torquez

yx

V(t)

B

Metal

Insu lator

W SM d

d0

(a)TCS AHEV(t)M B

• Helicity-induced magnetoresistenceand domain wall motion in Weyl semimetals

Yasufumi Araki(Ass. Prof.)Daichi Kurebayashi(D2) Koji Kobayashi(PD)Yuya Ominato(PD)Akihide Yoshida(M1)

Acknowledgement

References

[1] D. Kurebayashi and K. Nomura, J. Phys. Soc. Jpn. 83, 063709 (2014).[2] K. Nomura and D. Kurebayashi, Phys. Rev. Lett. 115, 127201 (2015).[3] D. Kurebayashi and K. Nomura, arXiv:1604.03326[4] Y. Araki and K. Nomura, Phys. Rev. B 93, 094438 (2016).[5] Y. Araki, A. Yoshida, and K. Nomura, Phys. Rev. B 93, 094438 (2016).

CollaboratorsIMR theory group

Documents

Topological Materials for Spintronis - JAEA...Topological insulator H surface k y x k x y Voltage difference between leftand right spin‐electricity conversion spin‐momentum locking